9.8 And the Delta V Formula?

[Camicus]

First off, I was debating whether to put this here or in the science discussion. Since we use to so much in KSP I put it here. (Sorry if it is in fact in the wrong section)

The formula that I have seen everywhere involves isp * 9.8, but what exactly does the 9.8 represent? From what I gathered, it is just isp * g and calculates the exhaust velocity. But why is it 9.8 instead of 9.81? Have I completely misunderstood something here?

Edited January 5, 2017 by Camicus

[Gaarst]

9.8 is 9.81 rounded to the 1st decimal, which itself is 9.80665 rounded to the 2nd decimal.

You usually don't need 5 decimal accuracy when planning a mission, hence the rounding.

[Vanamonde]

Science question moved to the science subforum. (Since it applies to real spaceflight as well.) 

[PB666]

ISP in secs is equal to exhausted velocity in meter per seconds.

X m/s / g {9.81 m * sec-2} = X/9.81  sec.  This has some relevance in the way you calculate when launching from earths surface.

Once you are in space better to convert the calculation into v.

 

[pincushionman]

It's a conversion factor, and it's to have a measurement of efficiency that's independent of your units system. It's actually not 9.8, it's g (standard acceleration from gravity at the Earth's surface), expressed in whatever units the rest of your measurements are in. So in metric you always use 9.8(0665…), regardless of what the actual local gravity is; in FPS it's 32.174, in IPS it's 386.1.

[cantab]

The "natural" formulation of the rocket equation is

Delta-V = effective exhaust speed x ln (full mass / dry mass).

For a perfect rocket engine it would just be the exhaust speed, the "effective" basically includes a correction for the details of the engine. And that's the equation several 19th and early 20th century scientists, most famously Tsiolkovsky, derived by considering the physics. You do the derivation considering things in empty space, so gravity doesn't come into it.

The problem is that as @pincushionman mentioned, exhaust speed is different in different units, and a certain spacefaring country refuses to universally adopt metric.

Hence the rocket equation is written instead using specific impulse (I_sp) in seconds, because everyone agrees what a second is. Specific impulse is defined quite simply - it's the impulse per unit of propellant, or equivalent the thrust divided by the rate of propellant flow. If you did the propellant by mass you would get a "specific impulse" in m/s - the same units as effective exhaust velocity and for a perfect rocket they are indeed equal, so it just swaps straight in. To get specific impulse in seconds you need to instead measure the propellant by weight, and that implies the measurement of that weight in a certain gravitational field.

And that's why we get g₀, Earth standard gravity, in the rocket equation. And why it's always the same whether you're orbiting Earth or Jupiter or Kerbin or Coruscant.

There is by the way a neat physical meaning to the specific impulse in seconds - it's the length of time the engine takes to burn a weight of fuel equal to its own thrust.